Context. Stellar rotation is of key importance in the formation process, the evolution, and the final fate of massive stars. Aims. We perform a reassessment of the empirical rotational properties of Galactic massive O-type stars using the results from a detailed analysis of ground-based multi-epoch optical spectra obtained in the framework of the IACOB & OWN surveys. Methods. Using high-quality optical spectroscopy, we established the velocity distribution for a sample of 285 apparently single and single-line spectroscopic binary (SB1) Galactic O-type stars. We also made use of the rest of the parameters from the quantitative spectroscopic analysis presented in prior IACOB papers (mainly Teff, log g, and multiplicity) to study the v sin i behavior and evolution from the comparison of subsamples in different regions of the spectroscopic Hertzsprung-Rusell diagram (sHRD). Our results are compared to the main predictions -regarding current and initial rotational velocities -of two sets of well-established evolutionary models for single stars, as well as from population synthesis simulations of massive stars that include binary interaction. Results. We reassess the known bimodal nature of the v sin i distribution, and find a non-negligible difference between the v sin i distribution of single and SB1 stars. We provide empirical evidence supporting the proposed scenario that the tail of fast rotators is mainly produced by binary interactions. Stars with extreme rotation (>300 km s-1) appear as single stars that are located in the lower zone of the sHRD. We notice little rotational braking during the main sequence, a braking effect independent of mass (and wind strength). The rotation rates of the youngest observed stars lean to an empirical initial velocity distribution with 20% of critical velocity. Lastly, a limit in v sin i detection below 40-50 km s-1 seems to persist, especially in the upper part of the sHRD, possibly associated with the effect of microturbulence in the measurement methodology used.